Omit Inconsequential Responses

We carefully administered questionnaires designed to measure respondents' degree of victimization. But soon discovered that analyzing responses to questions irrelevant to the respondent produced clinically misleading results.

--------------------------------------
|  RAW             OUTFIT   |Subject |
| SCORE  MEASURE MEAN-SQUARE|Response|
--------------------------------------
|     1   -2.47      7.79   | S 0001 |<-one severe experience
|     1   -2.47       .20   | M 1000 |<-one mild experience
--------------------------------------

The questionnaire includes 4 types of victimization. Respondent M had only experienced one type, the relatively mild "verbal pressure". Respondent S, however, had also experienced only one type, the more severe "physical force". Both respondents rated their experiences as "1" on a scale from "0" to "3". Since both raw scores are the same, 1 on the 4 items, their measures, based on the pre-calibrated items, are also the same. Yet their fit statistics are quite different, indicating the measure for Respondent S is problematic.

It is clear that "physical force" goes beyond "verbal pressure", so that we could edit the data by asserting that more extreme forms of victim abuse imply milder forms. Then remeasure the respondents, so obtaining more clinically reasonable measures and fit statistics.

A simpler approach is to bear in mind that the measure of interest corresponds to each respondent's most extreme form of victimization. It is easy to identify that measure on a map of the "Expected Ratings on Victimization Items".

         Expected Ratings on Victimization Item
 Mild                                           Severe
-5   -4    -3    -2    -1     0     1     2     3     4 *lt;-Logits
+-----+-----+-----+-----+-----+-----+-----+-----+-----+
                             0   :  X  :  2    :    3  Physical Force
                        0  :   1  :  2    :   3        Threats
                    0  :   1  :  2    :   3            Intoxication
     0  :   X  :  2    :   3                           Verbal Pressure
+-----+-----+-----+-----+-----+-----+-----+-----+-----+
            ^Respondent M(ild)      ^Respondent S(evere)

According to this Figure, Respondent M's mild victimization yields a measure of -3 logits, but Respondent S's severe victimization yields a measure of +1 logit. Now the measures make clinical sense. In other words, there is no need for us to be constrained by the printed form of the questionnaire, rather we can act as though each person was asked only one question: "Describe your worst victimization". Insisting that all data be analyzed in accordance with the ways they happen to have been collected manifests a "foolish consistency [which] is the hobgoblin of little minds" (Ralph Waldo Emerson, Conduct of Life: Self-Reliance).


Omit Inconsequential Responses. Karabatsos, G. … Rasch Measurement Transactions, 1997, 10:4 p. 523.

Please help with Standard Dataset 4: Andrich Rating Scale Model



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